Embodiments of the invention generally pertain to systems and methods for processing and coding data. In particular, embodiments of the invention pertain to systems and methods for encoding and decoding data.
Different codes can be used to encode data to achieve different results. One class of codes, called constrained codes, can be used to eliminate undesirable data patterns. A particular type of constrained codes, called run-length limited (RLL) codes, can be used to guarantee maximum and/or minimum transition spacing. RLL codes can be enhanced to provide DC-limited constraint in addition to run-length limited constraint. RLL codes are widely used in non-volatile storage drives, such as hard disk drives and digital optical discs, to prevent long stretches of no transitions, thus ensuring reliable timing information is available to the detector.
Another class of codes, called error-correcting codes (ECC), may be used to detect and/or correct errors. Error correcting codes are often used to correct errors which may occur during transmission or storage. Errors may occur for a number of reasons, including, for example, noise or interference, scratches on a CD, and/or other reasons. One type of ECC is known in the art as a Reed-Solomon (RS) code. A Reed-Solomon encoder receives original data and produces “redundant” or “parity” data based on the original data. The combination of the original data and the parity data is called a Reed-Solomon codeword. A RS codeword can be stored and/or communicated, during which errors may occur in the codeword, as described above. A Reed-Solomon decoder can process an erroneous version of a RS codeword to attempt to correct the errors and recover the original data.
Following the RS ECC encoder, the portion of RS ECC codeword that contains user data still satisfies the RLL constraint (if a systematic RS ECC encoder is used). However, the parity portion of RS ECC codeword might not have any RLL constraint. This in turn can present a problem on the decoder side: insufficient timing information and presence of catastrophic sequences in the RS parity portion can degrade detector performance. To avoid this difficulty, RS ECC redundancy has traditionally been encoded with another RLL code. The second RLL code has a much lower code rate, and is commonly referred to as a Low Rate RLL (LR RLL). Low rate RLL is used for RS ECC redundancy encoding because, on the decoder side, LR RLL has to be decoded prior to RS ECC decoder. Consequently LR RLL code can not have much error propagation, which dictates the use of low rate codes. In contrast, HR RLL code is decoded following the RS ECC decoder, and at this point either there are no errors (RS ECC was able to recover transmitted data) and so the error propagation of HR RLL is not an issue, or RS ECC failed and the sector must be re-transmitted.
There is a continuous interest in improving format efficiency by reducing the overhead of various codes used in the system.